OK, but do we necessarily just care about the central 95% range of the output? This calculation has the weird property that values in the tails of the input correspond to values in the middle of the output, and vice versa. If you follow the intuition that the range you specify in the input corresponds to the values you expect to see, the corresponding outputs would really include -inf and inf.

Now I'm realizing that this doesn't actually work, and even in more typical calculations the input values that produce the central 95% of the output are not necessarily drawn from the 95% CIs of the inputs. Which is fine and makes sense, but this example makes it very obvious how arbitrary it is to just drop the lowermost and uppermost 2.5%s rather than choosing any other 95/5 partition of the probability mass.

That may be true, but if you look at the distribution it puts out for this, it definitely smells funny. It looks like a very steep normal distribution, centered at 0 (ish). Seems like it should have two peaks? But maybe those are just getting compressed into one because of resolution of buckets?